7 papers
Apéry-type approximations and irrationality measures for certain -series
Junnosuke Koizumi, Anju Yokoi
We construct a three-parameter family of rational approximations to values of -hypergeometric series. Using these approximations, we prove that, for every integer with $|x|\…
At most 10 cylinders mutually touch: a Ramsey-theoretic approach
Travis Dillon, Junnosuke Koizumi, Sammy Luo
Littlewood asked for the maximum number of congruent infinite cylinders that can be arranged in so that every pair touches. We improve upon the proof of the seco…
A new upper bound for mutually touching infinite cylinders
Junnosuke Koizumi
Let denote the maximum number of congruent infinite cylinders that can be arranged in so that every pair of cylinders touches each other. Littlewood posed the qu…
Isosceles trapezoids of unit area with vertices in sets of infinite planar measure
Junnosuke Koizumi
Paul Erdős posed the question of whether every measurable planar set of infinite Lebesgue measure contains the four vertices of an isosceles trapezoid of unit area. In this paper,…
A note on the Erdős conjecture about square packing
Jineon Baek, Junnosuke Koizumi, Takahiro Ueoro
Let denote the maximum total length of the sides of squares packed inside a unit square. Erdős conjectured that . We show that the conjecture is true if we a…
Irreducibility of polynomials defining parabolic parameters of period 3
Junnosuke Koizumi, Yuya Murakami, Kaoru Sano +1
Morton and Vivaldi defined the polynomials whose roots are parabolic parameters for a one-parameter family of polynomial maps. We call these polynomials delta factors. They conject…
Quadratic residues and domino tilings
Yuhi Kamio, Junnosuke Koizumi, Toshihiko Nakazawa
The formula for the number of domino tilings due to Kasteleyn and Temperley-Fisher is strikingly similar to Eisenstein's formula for the Legendre symbol. We study the connection be…